Let \(\delta \in (0,1)\)  be a confidence parameter and \({\mu }\)  be a bandit problem. Considering a \(\delta \) -PAC strategy, we can apply transportation Lemma 1 of [1]} to obtain
\(\sum _{a\in [K]}\frac{(\mu _a-\lambda _a)^2}{2}\mathbb {E}[N_a] \ge \operatorname{kl}(\delta ,\,1-\delta )\) 
